Michio Kaku and Einstein

I watched a video of Michio Kaku saying that according the Einstein's equations of black holes, physics literally breaks down into nothing. I just wanted to ask how accurate the things he says are.

For example he states that the mass of the blackhole being M and R describes the distance from the blackhole, but when R is equal to 0. You simply get infinity.

So he states that the very centre of a blackhole, according to Einstein's equations gravity would be infinite and time itself completely stops. Also he says that all the mass of a blackhole, is contained within an infinitely small, infinitely dense point that takes up exactly 0 space at all.

So if this is true, could we argue that the matter simple dissapears? As in literally no longer exists?

Maybe blackholes are "gods" way of cleaning up the universe, getting rid of things he no longer likes the look of :D

What is the quantum mechanical reason that would keep physical matter from contracting to infinity or near infinity in the presence of immense gravity? Classical matter can't contract anywhere near such proportions but where can i find such classical matter made of classical particles?

So he states that the very centre of a blackhole, according to Einstein's equations gravity would be infinite and time itself completely stops.

He's taking a small bet and imo he knows what he stakes. He's bold and AFAIK Einstein has been his role model and he'd rather be in the innovators camp than in the 'don't know camp'. It's speculation both ways - that there could be an extremely dense classical-like core at the center of a black-hole or 'size' that converges to infinity.

So if this is true, could we argue that the matter simple dissapears?

Why is this more bothersome than space(time) contracting in the presence of large mass?